(x+1)(x^2-1)-x^3=-1

Solution for (x+1)(x^2-1)-x^3=-1 equation:

Simplifying
(x + 1)(x2 + -1) + -1x3 = -1

Reorder the terms:
(1 + x)(x2 + -1) + -1x3 = -1

Reorder the terms:
(1 + x)(-1 + x2) + -1x3 = -1

Multiply (1 + x) * (-1 + x2)
(1(-1 + x2) + x(-1 + x2)) + -1x3 = -1
((-1 * 1 + x2 * 1) + x(-1 + x2)) + -1x3 = -1
((-1 + 1x2) + x(-1 + x2)) + -1x3 = -1
(-1 + 1x2 + (-1 * x + x2 * x)) + -1x3 = -1
(-1 + 1x2 + (-1x + x3)) + -1x3 = -1

Reorder the terms:
(-1 + -1x + 1x2 + x3) + -1x3 = -1
(-1 + -1x + 1x2 + x3) + -1x3 = -1

Combine like terms: x3 + -1x3 = 0
-1 + -1x + 1x2 + 0 = -1
-1 + -1x + 1x2 = -1

Add '1' to each side of the equation.
-1 + -1x + 1 + 1x2 = -1 + 1

Reorder the terms:
-1 + 1 + -1x + 1x2 = -1 + 1

Combine like terms: -1 + 1 = 0
0 + -1x + 1x2 = -1 + 1
-1x + 1x2 = -1 + 1

Combine like terms: -1 + 1 = 0
-1x + 1x2 = 0

Solving
-1x + 1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-1 + x) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0
Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve:

Simplifying
-1 + x = 0

Solving
-1 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + x = 0 + 1
x = 0 + 1

Combine like terms: 0 + 1 = 1
x = 1

Simplifying
x = 1
Solution
x = {0, 1}